@article{bbphpaper,
title = "BBPH: Using progressive hedging within branch and bound to solve multi-stage stochastic mixed integer programs ",
journal = "Operations Research Letters ",
volume = "",
number = "",
pages = " - ",
year = "2016",
note = "",
issn = "0167-6377",
doi = "http://dx.doi.org/10.1016/j.orl.2016.11.006",
url = "http://www.sciencedirect.com/science/article/pii/S0167637716302152",
author = "Jason Barnett and Jean-Paul Watson and David L. Woodruff",
keywords = "Stochastic programming",
keywords = "Progressive hedging",
keywords = "Branch and bound "
}


@article{part2,
author = {Kwok Cheung and Dinakar Gade and Cesar Silva Monroy and Sarah M. Ryan and 
Jean-Paul Watson and Roger J.-B. Wets and David L. Woodruff}, 
title = {Scalable Stochastic Unit Commitment, Part 2: Solver Performance},
journal = {Energy Systems},
year = {to appear} 
}

@article{claireLetters,
title={Integration of progressive hedging and dual decomposition in stochastic integer programs},
author = {G Guo and G Hackebeil and SM Ryan and JP Watson and DL Woodruff},
journal = {Operations Research Letters},
volume =  {43},
year = {2015},
pages = { 311--316}
}

@article{bounds,
author={D. Gade and G. Hackebeil and S.M. Ryan and J.P. Watson and R.J.B. Wets and D.L. Woodruff},
title={Obtaining Lower Bounds From the Progressive Hedging Algorithm for Stochastic Mixed-Integer Programs},
journal={Mathematical Programming, Series B},
year={2016}
}

@book{BBText,
   author={G. Nemhauser and L.  Wolsey},
   year = {1988},
   Title ={ Integer and Combinatorial Optimization},
   Publisher = {Wiley-Interscience}
}


@MISC{SIPB9607,
          author = {Maarten H. {van der Vlerk}},
          title = {Stochastic Integer Programming Bibliography},
          year = {1996-2007},
          howpublished = {World Wide Web,
                          \url{http://www.eco.rug.nl/mally/biblio/sip.html}}
}
@article{held2005decomposition,
  title={A decomposition algorithm applied to planning the interdiction of stochastic networks},
  author={Held, Harald and Hemmecke, Raymond and Woodruff, David L},
  journal={Naval Research Logistics (NRL)},
  volume={52},
  number={4},
  pages={321--328},
  year={2005},
  publisher={Wiley Online Library}
}
@article{cormican1998stochastic,
  title={Stochastic network interdiction},
  author={Cormican, Kelly J and Morton, David P and Wood, R Kevin},
  journal={Operations Research},
  volume={46},
  number={2},
  pages={184--197},
  year={1998},
  publisher={INFORMS}
}

@article{janjarassuk2008reformulation,
  title={Reformulation and sampling to solve a stochastic network interdiction problem},
  author={Janjarassuk, Udom and Linderoth, Jeff},
  journal={Networks},
  volume={52},
  number={3},
  pages={120--132},
  year={2008},
  publisher={Wiley Online Library}
}

@article{santoso2005stochastic,
  title={A stochastic programming approach for supply chain network design under uncertainty},
  author={Santoso, Tjendera and Ahmed, Shabbir and Goetschalckx, Marc and Shapiro, Alexander},
  journal={European Journal of Operational Research},
  volume={167},
  number={1},
  pages={96--115},
  year={2005},
  publisher={Elsevier}
}

@article{KautWallace07,
title = "Evaluation of scenario-generation methods for stochastic programming",
author = "Michal Kaut and Wallace, {Stein W.}",
year = "2007",
volume = "3",
number = "2",
pages = "257--271",
journal = "Pacific Journal of Optimization",
}
@incollection{EichhornHeitschRomisch11,
year={2010},
isbn={978-3-642-12685-7},
booktitle={Handbook of Power Systems II},
series={Energy Systems},
editor={Rebennack, Steffen and Pardalos, Panos M. and Pereira, Mario V. F. and Iliadis, Niko A.},
doi={10.1007/978-3-642-12686-4_15},
title={Stochastic Optimization of Electricity Portfolios: Scenario Tree Modeling and Risk Management},
url={http://dx.doi.org/10.1007/978-3-642-12686-4_15},
publisher={Springer Berlin Heidelberg},
keywords={Electricity; Energy trading; Multiperiod risk; Polyhedral risk functionals; Power portfolio; Risk management; Scenario reduction; Scenario tree approximation; Stochastic programming},
author={Eichhorn, Andreas and Heitsch, Holger and R{\"o}misch, Werner},
pages={405-432},
language={English}
}

@incollection{PflugPichler11,
author = {George Ch. Pflug and Alois Pichler},
editor = {Marida Bertocchi and Giorgio Consigli and Michael A.H. Dempster},
booktitle = {Stochastic Optimization Methods in Finance and Energy},
title = {Approximations for Probability Distributions and Stochastic Optimization Problems},
publisher = {Springer},
year = {2011},
volume = {163},
series = {International Series in Operations Research and Management Science},
}

@incollection{W75,
  title={On the relation between stochastic and deterministic optimization},
  author={Wets, Roger J-B},
  booktitle={Control Theory, Numerical Methods and Computer Systems Modelling},
  pages={350--361},
  year={1975},
  publisher={Springer Berlin Heidelberg}
}
@incollection{W89,
  title={The aggregation principle in scenario analysis and stochastic optimization},
  author={Wets, Roger J-B},
  booktitle={Algorithms and Model Formulations in Mathematical Programming},
  editor={Wallace, Stein W},
  pages={91--113},
  year={1989},
  publisher={Springer-Verlag}
}
@article{NtaimoSen,
  title={The million-variable ``march'' for stochastic combinatorial optimization},
  author={Ntaimo, Lewis and Sen, Suvrajeet},
  journal={Journal of Global Optimization},
  volume={32},
  pages={385--400},
  year={2005},
  publisher={Springer}
}
@article{Takriti_etal,
  title={A stochastic model for the unit commitment problem},
  author={Takriti, Samer and Birge, John R and Long, Eric},
  journal={IEEE Transactions on Power Systems},
  volume={11},
  number={3},
  pages={1497--1508},
  year={1996},
  publisher={IEEE}
}
@article{Ruiz_etal09,
  title={Uncertainty management in the unit commitment problem},
  author={Ruiz, P. A. and Philbrick, R. C. and Zack, E. and Cheung K. W. and Sauer, P.W.},
  journal={IEEE Transactions on Power Systems},
  volume={24},
  number={2},
  pages={642--651},
  year={2009},
  publisher={IEEE}
}
@article{Papa_Oren13,
  title={Multiarea stochastic unit commitment for high wind penetration in a transmission constrained network},
  author={Papavasiliou, Anthony and Oren, Shmuel S.},
  journal={Operations Research},
  volume={61},
  number={3},
  pages={578--592},
  year={2013},
  publisher={INFORMS}
}
@article{ATS04,
  title={A finite branch and bound algorithm for two-stage stochastic integer programs},
  author={Ahmed, Shabbir and Tawarmalani, Mohit and Sahinidis, Nikolaus V},
  journal={Mathematical Programming, Series A},
  volume={100},
  number = {2},
  pages={355--377},
  year={2004},
  publisher={Springer}
}

@TechReport{AhmedBB,
  author={Shabbir Ahmed},
  year = 2013,
  title = {A scenario decomposition algorithm for 0-1 stochastic programs},
  institution = {ISYE, Georgia Tech}
}
  

@article{LW96,
  title={Progressive hedging and tabu search applied to mixed integer (0,1) multistage stochastic programming},
  author={L{\o}kketangen, Arne and Woodruff, David L},
  journal={Journal of Heuristics},
  volume={2},
  pages={111--128},
  year={1996},
  publisher={Kluwer}
}
@article{RW91,
  title={Scenarios and policy aggregation in optimization under uncertainty},
  author={Rockafellar, R Tyrrell and Wets, Roger J-B},
  journal={Mathematics of Operations Research},
  volume={16},
  number={1},
  pages={119--147},
  year={2004},
  publisher={INFORMS}
}

% dlw Jan 2016: fix the entry then delete this comment!!
@article{Escudero09,
author="Escudero, Laureano F.
and Gar{\'i}n, Araceli
and Merino, Mar{\'i}a
and P{\'e}rez, Gloria",
title="BFC-MSMIP: an exact branch-and-fix coordination approach for solving multistage stochastic mixed 0--1 problems",
journal="TOP",
year="2009",
volume="17",
number="1",
pages="96--122",
abstract="We present an exact algorithmic framework, so-called BFC-MSMIP, for optimizing multistage stochastic mixed 0--1 problems with complete recourse. The uncertainty is represented by using a scenario tree and lies anywhere in the model. The problem is modeled by a splitting variable representation of the Deterministic Equivalent Model of the stochastic problem, where the 0--1 variables and the continuous variables appear at any stage. The approach uses the Twin Node Family concept within the algorithmic framework, so-called Branch-and-Fix Coordination, for satisfying the nonanticipativity constraints in the 0--1 variables. Some blocks of additional strategies are used in order to show the performance of the proposed approach. The blocks are related to the scenario clustering, the starting branching and the branching order strategies, among others. Some computational experience is reported. It shows that the new approach obtains the optimal solution in all instances under consideration.",
issn="1863-8279",
doi="10.1007/s11750-009-0083-6",
url="http://dx.doi.org/10.1007/s11750-009-0083-6"
}

@article{CS98,
  title={Dual decomposition in stochastic integer programming},
  author={Car{\o}e, Claus C and Schultz, R{\"u}diger},
  journal={Operations Research Letters},
  volume={24},
  number={1},
  pages={37--45},
  year={1999},
  publisher={Elsevier}
}
@misc{H11,
  title={The ConicBundle Library for Convex Optimization},
  author={Christoph Helmberg},
  year = {2011},
  howpublished={\url{http://www-user.tu-chemnitz.de/~helmberg/index.html}}
}

@article{MG11,
  title={User's Guide to ddsip--A {C} Package for the Dual Decomposition of Two-Stage Stochastic Programs with Mixed-Integer Recourse},
  author={M{\"a}rkert, A and Gollmer, R},
  journal={Department of Mathematics, University of Duisburg-Essen},
  year={2008}
}

@article{LMPS13,
  title={On parallelizing dual decomposition in stochastic integer programming},
  author={Lubin, Miles and Martin, Kipp and Petra, Cosmin and Sand{\i}k{\c{c}}{\i}, Burhaneddin},
  journal={Operations Research Letters},
  volume={41},
  number={3},
  pages={252--258},
  year={2013}
}

@article{GK87,
  title={Lagrangean decomposition: a model yielding stronger Lagrangean bounds},
  author={Guignard, Monique and Kim, Siwhan},
  journal={Mathematical programming},
  volume={39},
  number={2},
  pages={215--228},
  year={1987},
  publisher={Springer}
}

@book{NW88,
  title={Integer and combinatorial optimization},
  author={Nemhauser, George L and Wolsey, Laurence A},
  volume={18},
  year={1988},
  publisher={Wiley New York}
}

@article{M74,
  title={On the existence of optimal solutions to integer and mixed-integer programming problems},
  author={Meyer, Robert R},
  journal={Mathematical Programming},
  volume={7},
  number={1},
  pages={223--235},
  year={1974},
  publisher={Springer}
}

@article{DW60,
  title={Decomposition principle for linear programs},
  author={Dantzig, George B and Wolfe, Philip},
  journal={Operations research},
  volume={8},
  number={1},
  pages={101--111},
  year={1960},
  publisher={INFORMS}
}

@book{S85,
  title={Minimization methods for non-differentiable functions},
  author={Shor, Naum Zuselevich and Kiwiel, Krzysztof C and Ruszczynski, A},
  volume={3},
  year={1985},
  publisher={Springer-Verlag Berlin}
}

@book{HL93,
  title={Convex analysis and minimization algorithms},
  author={Hiriart-Urruty, Jean-Baptiste and Lemar{\'e}chal, Claude},
  year={1993},
  publisher={Springer}
}

@article{LS04,
  title={A branch-and-price algorithm for multistage stochastic integer programming with application to stochastic batch-sizing problems},
  author={Lulli, Guglielmo and Sen, Suvrajeet},
  journal={Management Science},
  volume={50},
  number={6},
  pages={786--796},
  year={2004},
  publisher={INFORMS}
}

@article{WW11,
  title={Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems},
  author={Watson, Jean-Paul and Woodruff, David L},
  journal={Computational Management Science},
  volume={8},
  number={4},
  pages={355--370},
  year={2011},
  publisher={Springer}
}

@article{CA06,
  title={A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem},
  author={Carri{\'o}n, Miguel and Arroyo, Jos{\'e} M},
  journal={Power Systems, IEEE Transactions on},
  volume={21},
  number={3},
  pages={1371--1378},
  year={2006},
  publisher={IEEE}
}

@article{ST07,
  title={Dynamic testing of wholesale power market designs: An open-source agent-based framework},
  author={Sun, J. and Tesfatsion, L.},
  journal={Computational Economics},
  volume={30},
  number={3},
  pages={291--327},
  year={2007},
  publisher={Springer}
}
@article{MV91a,
  title={Solving multistage stochastic networks: an appplication of scenario aggregation},
  author={Mulvey, John M and Vladimirou, Hercules},
  journal={Networks},
  volume={21},
  pages={619--643},
  year={1991},
  publisher={John Wiley & Sons}
}
@article{MV91b,
  title={Applying the progressive hedging algorithm to stochastic generalized networks},
  author={Mulvey, John M and Vladimirou, Hercules},
  journal={Annals of Operations Research},
  volume={31},
  pages={399--424},
  year={1991},
  publisher={Baltzer}
}
@inproceedings{RRWWM13,
  title={Toward scalable, parallel progressive hedging for stochastic unit commitment},
  author={Ryan, Sarah M and Wets, Roger J-B and Woodruff, David L and Silva-Monroy, C{\'e}sar and Watson, Jean-Paul},
  booktitle={Power and Energy Society General Meeting, 2013 IEEE},
  year = {2013},
  organization={IEEE}
}

@article{guo2015integration,
  title={Integration of progressive hedging and dual decomposition in stochastic integer programs},
  author={Guo, Ge and Hackebeil, Gabriel and Ryan, Sarah M and Watson, Jean-Paul and Woodruff, David L},
  journal={Operations Research Letters},
  volume={43},
  number={3},
  pages={311--316},
  year={2015},
  publisher={North-Holland}
}


@article{pyspmpc,
  title={{PySP}: Modeling and solving stochastic programs in {Python}},
  author={Watson, J.P. and Woodruff, D.L. and Hart, W.E.},
  journal={Mathematical Programming Computation},
  volume={4},
  number={2},
  year={2012},
  publisher={Springer}
}
@article{pyomompc,
  title={{Pyomo}: Modeling and solving mathematical programs in {Python}},
  author={Hart, W.E. and Watson, J.P. and Woodruff, D.L.},
  journal={Mathematical Programming Computation},
  volume={3},
  number={3},
  year={2011},
  publisher={Springer}
}
@article{crainicetal14,
  title={Scenario grouping in a progressive hedging-based meta-heuristics for stochastic network design},
  author={Crainic, T.G. and Hewitt, M. and Rei, W.},
  journal={Computers and Operations Research},
  volume={43},
  pages={90--99},
  year={2014},
  publisher={Elsevier}
}
@article{boydetal11,
  title={Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers},
  author={Boyd, S. and Parihk, N. and Chu, E. and Peleato, B. and Eckstein, J.},
  journal={Foundations and Trends in Machine Learning},
  volume={3},
  issue={1},
  year={2011}
}

@article{WWW10,
 author = {J.-P. Watson and R. J.-B. Wets and D.L. Woodruff},
 title = {Scalable Heuristics for a Class of Chance-Constrained Stochastic Programs},
 journal = {INFORMS Journal on Computing},
 issue_date = {Fall 2010},
 volume = {22},
 number = {4},
 month = oct,
 year = {2010},
 issn = {1526-5528},
 pages = {543--554},
 numpages = {12},
 url = {http://dx.doi.org/10.1287/ijoc.1090.0372},
 doi = {10.1287/ijoc.1090.0372},
 acmid = {1878527},
 publisher = {INFORMS},
 address = {Institute for Operations Research and the Management Sciences (INFORMS), 
    Linthicum, Maryland, USA},
} 

@Article{Ruszczynski,
  author = 	 {A. Ruszczy{\'n}ski},
  title = 	 {Probabilistic Programming with Discrete Distributions and Precedence Constrained Knapsack Polyhedra},
  journal = 	 {Mathematical Programming},
  year = 	 {2002},
  volume = 	 {93},
  pages = 	 {195--215}
}

﻿@Article{Fan2008,
author="Fan, Yueyue
and Liu, Changzheng",
title="Solving Stochastic Transportation Network Protection Problems Using the Progressive Hedging-based Method",
journal="Networks and Spatial Economics",
year="2008",
volume="10",
number="2",
pages="193--208",
abstract="This research focuses on pre-disaster transportation network protection against uncertain future disasters. Given limited resources, the goal of the central planner is to choose the best set of network components to protect while allowing the network users to follow their own best-perceived routes in any resultant network configuration. This problem is formulated as a two-stage stochastic programming problem with equilibrium constraints, where the objective is to minimize the total expected physical and social losses caused by potential disasters. Developing efficient solution methods for such a problem can be challenging. In this work, we will demonstrate the applicability of progressive hedging-based method for solving large scale stochastic network optimization problems with equilibrium constraints. In the proposed solution procedure, we solve each modified scenario sub-problem as a mathematical program with complementary constraints and then gradually aggregate scenario-dependent solutions to the final optimal solution.",
issn="1572-9427",
doi="10.1007/s11067-008-9062-y",
url="http://dx.doi.org/10.1007/s11067-008-9062-y"
}

@article{Crainic2011,
author = {Crainic, Teodor Gabriel and Fu, Xiaorui and Gendreau, Michel and Rei, Walter and Wallace, Stein W.},
title = {Progressive hedging-based metaheuristics for stochastic network design},
journal = {Networks},
volume = {58},
number = {2},
publisher = {Wiley Subscription Services, Inc., A Wiley Company},
issn = {1097-0037},
url = {http://dx.doi.org/10.1002/net.20456},
doi = {10.1002/net.20456},
pages = {114--124},
keywords = {stochastic network design, metaheuristics, progressive hedging, lagrangean relaxation},
year = {2011},
}

@article{Crainic2014,
 author = {Crainic, Teodor Gabriel and Hewitt, Mike and Rei, Walter},
 title = {Scenario Grouping in a Progressive Hedging-based Meta-heuristic for Stochastic Network Design},
 journal = {Comput. Oper. Res.},
 issue_date = {March, 2014},
 volume = {43},
 month = mar,
 year = {2014},
 issn = {0305-0548},
 pages = {90--99},
 numpages = {10},
 url = {http://dx.doi.org/10.1016/j.cor.2013.08.020},
 doi = {10.1016/j.cor.2013.08.020},
 acmid = {2565219},
 publisher = {Elsevier Science Ltd.},
 address = {Oxford, UK, UK},
 keywords = {Machine learning, Network design, Progressive hedging, Scenario clustering, Stochastic programs},
} 

@article{Hvattum2006,
author = {Lars M. Hvattum and Arne Løkketangen and Gilbert Laporte},
title = {Solving a Dynamic and Stochastic Vehicle Routing Problem with a Sample Scenario Hedging Heuristic},
journal = {Transportation Science},
volume = {40},
number = {4},
pages = {421-438},
year = {2006},
doi = {10.1287/trsc.1060.0166},

URL = { 
        http://dx.doi.org/10.1287/trsc.1060.0166
    
},
eprint = { 
        http://dx.doi.org/10.1287/trsc.1060.0166
    
}

}

@Article{Hvattum2008,
author="Hvattum, Lars Magnus
and L{\o}kketangen, Arne",
title="Using scenario trees and progressive hedging for stochastic inventory routing problems",
journal="Journal of Heuristics",
year="2008",
volume="15",
number="6",
pages="527--557",
abstract="The Stochastic Inventory Routing Problem is a challenging problem, combining inventory management and vehicle routing, as well as including stochastic customer demands. The problem can be described by a discounted, infinite horizon Markov Decision Problem, but it has been showed that this can be effectively approximated by solving a finite scenario tree based problem at each epoch. In this paper the use of the Progressive Hedging Algorithm for solving these scenario tree based problems is examined. The Progressive Hedging Algorithm can be suitable for large-scale problems, by giving an effective decomposition, but is not trivially implemented for non-convex problems. Attempting to improve the solution process, the standard algorithm is extended with locking mechanisms, dynamic multiple penalty parameters, and heuristic intermediate solutions. Extensive computational results are reported, giving further insights into the use of scenario trees as approximations of Markov Decision Problem formulations of the Stochastic Inventory Routing Problem.",
issn="1572-9397",
doi="10.1007/s10732-008-9076-0",
url="http://dx.doi.org/10.1007/s10732-008-9076-0"
}

@article{dosSantos2009546,
title = "Practical aspects in solving the medium-term operation planning problem of hydrothermal power systems by using the progressive hedging method ",
journal = "International Journal of Electrical Power \& Energy Systems ",
volume = "31",
number = "9",
pages = "546 - 552",
year = "2009",
note = "Power Systems Computation Conference (PSCC) 2008Power Systems Computation Conference (PSCC) 200816th Power Systems Computation Conference (PSCC), 2008 ",
issn = "0142-0615",
doi = "http://dx.doi.org/10.1016/j.ijepes.2009.03.032",
url = "http://www.sciencedirect.com/science/article/pii/S0142061509000726",
author = "Marcelo L.L. dos Santos and Edson Luiz da Silva and Erlon Cristian Finardi and Raphael E.C. Gonçalves",
keywords = "Hydrothermal systems",
keywords = "Medium-term operating planning",
keywords = "Stochastic programming",
keywords = "Progressive hedging "
}

